library(tidyverse)
library(magrittr)
# library(locfit) #for chemdiab data set. Local regression, likelihood and density estimation.
# data(chemdiab) 
# 
# dat <- as_tibble(chemdiab)
# 
# library(ks)
#Kernel smoothers for univariate and multivariate data, including densities, density derivatives, cumulative distributions, clustering, classification, density ridges, significant modal regions, and two-sample hypothesis tests.

What‘s TDA?

TDA is a yet little-known data science tool that allows to effectively work with high-dimensional data. In TDA data is considered as a mathematical object and the aim is to characterize the shape of this object using tools taken from the subfield of Mathematics called Topology.

How to use it?

TDA is able to render high dimensional data in a more comprehensible from and one way to do this is by representing data as a topological network. This kind of network provides an insightful segmentation of the data that, in turn, offers the opportunity to identify relevant topological features. These topological attributes can then be considered to develop highly tuned Machine Learning models. And this is only the beginning (persistent homology is next!)

The steps of the mapper algorithm:

Project a high dimensional dataset through functions, called lenses, in a lower dimensional space.
Cover this projection with overlapping hypercubes (n-dimensional analogue of a square in 2-dimensions).
Cluster the points in the original higher dimensional feature space hypercube by hypercube, i.e., hypercube by hypercube, cluster the inverse image (through the lenses) of the hypercube in the lower dimensional space.
The clusters become nodes of a graph.
Due to the overlap, a single point can appear in multiple nodes, when this happens, then there will be drawn an edge between these nodes.

The data set

What it is etc. Where to get it.

# norm_dat <- dat %>% mutate_if(is.numeric, scale, center = FALSE)
# 
# dist_dat <- norm_dat %>% select_if(is.numeric) %>% stats::dist()

df <- readr::read_csv("data.csv") 

# feature_names <- df %>% names() %>% setdiff(., c("id", "diagnosis"))

Y <- df %>% mutate(diagnosis = ifelse(diagnosis == "M", 1, 0)) %>% pull(diagnosis)

X <- df %>% select(-c("id", "diagnosis")) %>% mutate_all(., replace_na, replace = 0) %>% mutate_all(., scale, center=TRUE)

# Create a custom 1-D lens with Isolation Forest

scale_zero_to_one <- function(vector){

  a <- vector - min(vector)
  b <- max(vector) - min(vector)

  return(a/b)
}

model <- solitude::isolationForest$new(num_trees = 2500, mtry = 20)
model$fit(X)
lens1 <- model$scores$anomaly_score %>% scale_zero_to_one()

#calc euclidean dist among rows

# apply(X, 2, function(x) sqrt(sum(x^2)))  # The L2-norm

# lens2 <- df %>%
#   select(-diagnosis) %>%
#   group_nest(id) %>%
#   mutate(data = map(data, ~norm(as.matrix(.x), type = "2"))) %>%
#   unnest(data) %>%
#   pull(data) %>% scale_zero_to_one()

cl <- dbscan::hdbscan(X, minPts = 5)
lens2 <- cl$outlier_scores

lens <- cbind(lens1, lens2)

tibble(lens[,1], lens[,2], Y) %>% ggplot(aes(x=lens1, y=lens2, color=as.factor(Y))) + geom_point()

dist_X <- dist(X) # distance matrix

the_map <- TDAmapper::mapper(
           dist_object = dist_X,
           filter_values = list(lens[,1], lens[,2]),
           num_intervals = c(10 ,10), # 1 value for each lens.
           percent_overlap = 50,
           num_bins_when_clustering = 5)

Because we use two lenses, our data set will be projected into a two dimensional space.

dist_object: A matrix containing distance information between observations (rows) of the data.
filter_values: Here the chosen lenses are supplied to the mapper function.
num_intervals: The more intervals, the more granularity for producing covers. 10 by 10 intervals will produce a cover of 100 “squares” in two dimensions. This will lead to more nodes in the end. The clustering will be applied to each element (here, the resutling squares) of the pullback image of the cover. The clusters are the nodes of the graph. This is why the mapper is called a local clustering algorithm (guided by the lenses).
percent_overlap: The more percent overlap, the more edges will appear in the network. As the percent overlap increases, also the likelihood of having nodes that share at least one observation increases and each time two nodes have a intersection, an edge will appear in the network.
num_bins_when_clustering: The amount of clusters per element of the cover. The more clusters are allowed, the more nodes. The clustering algorithm used in the TDAmapper package is {stats::hclust()}.

For more information on “mapper”, see here: (Singh, Mémoli, and Carlsson 2007)

Linking the output from the mapper to your data set.

Also say why the hell you do this.

# #### Relating node information to the original data frame.

df %<>% mutate(rows = rownames(.) %>% as.factor())  %>% 
  add_column("iso_forest" = lens1, 
             "outlier_score" =  lens2)

df_nest <- df %>% mutate(diagnosis = ifelse(diagnosis == "M", 1, 0)) %>% group_nest(rows)


MapperNodes <- TDAmapper::mapperVertices(the_map, df$rows)
## it is a string mixed with numericals. The output of the mapper function is more useful as it 
## 



df_nodes <- the_map %>% as.list() %>% 
  pluck("points_in_vertex") %>% 
  tibble() %>% rename(rows = ".") %>% 
  mutate(Nodename = paste0("N", seq(1, length(MapperNodes$Nodename)))) %>% 
  unnest(rows) %>%
  mutate(rows = as.factor(rows)) %>%
  left_join(df_nest, ., by="rows") %>%
  unnest(data)


##example what could be done now:
# df_nodes  %>% group_by(Nodename) %>%
#    summarise_all(mean) %>% 
#   ggplot(aes(x=smoothness_mean, y=outlier_score, color=iso_forest)) + geom_point()


####

Visualizations

D3 (not recommended)

Mode <- function(x) {
  ux <- unique(x)
  ux[which.max(tabulate(match(x, ux)))]
}

MapperNodes <- TDAmapper::mapperVertices(the_map, df$rows)
MapperLinks <- TDAmapper::mapperEdges(the_map)

nodes <- the_map$points_in_vertex

# group <-  map_dbl(nodes, ~Mode(Y[.x])) 
# MapperNodes$Nodegroup <- ifelse(group==1, "Cancer", "Healty")
# colore <- sort(unique(map_dbl(nodes, ~mean(Y[.x])*100)))
networkD3::forceNetwork(
  Nodes = MapperNodes, 
  Links = MapperLinks, 
  Source = "Linksource", 
  Target = "Linktarget",
  Value = "Linkvalue",
  NodeID = "Nodename",
  Nodesize = "Nodesize",
  Group = "Nodegroup",
  # legend = "False",
  charge = -40,
  height = 1000, # Size of the plot (vertical)
  width = 1500,  # Size of the plot (horizontal)
   # linkDistance = networkD3::JS("function(d) { return 10*d.value; }"), # Function to determine distance between any two nodes, uses variables already defined in forceNetwork function (not variables from a data frame)
  # linkWidth = networkD3::JS("function(d) { return d.value/5; }"),# Function to determine link/edge thickness, uses variables already defined in forceNetwork function (not variables from a data frame)
   opacity = 5, # opacity
    zoom = TRUE) # ability to zoom when click on the node)

ggnetwork

Linking the data and mapper output to the visualization

library(network)
# library(sna)
# library(intergraph) #makes igraph compatible
library(ggplot2)
library(ggnetwork)
library(kableExtra)

adja_matrix <- the_map$adjacency
nodes <- the_map$points_in_vertex
# MapperNodes <- TDAmapper::mapperVertices(the_map, df$id)
Nodename <- paste0("N", seq(1, length(nodes)))

#WHAT DOES NODEGROUP MEAN??????? 

net_df <- network(adja_matrix, directed = FALSE, vertex.attr = list("Nodename" = Nodename)) %>%
  ggnetwork()
# df_nodes <- n select(-vertex.names) %>% left_join(., df_nodes, by="Nodename")


#here you can compute whatever you need (example: mean) connection between data and vis
mean_dat <- df_nodes %>% group_by(Nodename) %>% summarize_all(mean)

combined_dat <- left_join(net_df, mean_dat, by="Nodename")



kable(combined_dat) %>%
  kable_styling("striped", full_width = F) %>%
  kable_styling() %>%
  scroll_box(width = "100%", height = "500px")

x	y	Nodename	vertex.names	xend	yend	rows	id	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave points_mean	symmetry_mean	fractal_dimension_mean	radius_se	texture_se	perimeter_se	area_se	smoothness_se	compactness_se	concavity_se	concave points_se	symmetry_se	fractal_dimension_se	radius_worst	texture_worst	perimeter_worst	area_worst	smoothness_worst	compactness_worst	concavity_worst	concave points_worst	symmetry_worst	fractal_dimension_worst	iso_forest	outlier_score
0.0313333	0.5589993	N52	52	0.0832546	0.4545349	NA	8810955.0	1.0000000	14.19000	23.81000	92.87000	610.7000	0.0946300	0.1306000	0.1115000	0.0646200	0.2235000	0.0643300	0.4207000	1.8450000	3.534000	31.00000	0.0108800	0.0371000	0.0368800	0.0162700	0.0449900	0.0047680	16.86000	34.85000	115.00000	811.3000	0.1559000	0.4059000	0.3744000	0.1772000	0.4724000	0.1026000	0.4132161	0.6996134
0.0810987	0.6660942	N53	53	0.1033860	0.5708874	NA	4906037.0	0.6666667	14.15000	20.07333	92.56333	648.4333	0.0938433	0.1285200	0.1228833	0.0643300	0.1986167	0.0640650	0.6660000	1.4766500	4.544667	57.24333	0.0109600	0.0501320	0.0608483	0.0225338	0.0369267	0.0054958	16.47233	25.39667	108.46833	864.7167	0.1242667	0.2655333	0.2933833	0.1322667	0.3321333	0.0841483	0.4943539	0.7244737
0.0810987	0.6660942	N53	53	0.0313333	0.5589993	NA	4906037.0	0.6666667	14.15000	20.07333	92.56333	648.4333	0.0938433	0.1285200	0.1228833	0.0643300	0.1986167	0.0640650	0.6660000	1.4766500	4.544667	57.24333	0.0109600	0.0501320	0.0608483	0.0225338	0.0369267	0.0054958	16.47233	25.39667	108.46833	864.7167	0.1242667	0.2655333	0.2933833	0.1322667	0.3321333	0.0841483	0.4943539	0.7244737
0.0832546	0.4545349	N46	46	0.1886496	0.3492252	NA	18666783.0	0.5625000	14.25956	19.22750	93.63375	657.7750	0.1003150	0.1230275	0.1143862	0.0580681	0.2028312	0.0659688	0.4925000	1.4001125	3.524875	46.62500	0.0098769	0.0376344	0.0438537	0.0151248	0.0270600	0.0057202	16.41937	24.51187	109.17375	870.0562	0.1336938	0.2839950	0.3022356	0.1227006	0.3150938	0.0884225	0.3771646	0.6387061
0.1033860	0.5708874	N47	47	0.1689766	0.4723279	NA	18230737.0	0.6285714	15.49009	20.75429	101.91514	804.6686	0.1006531	0.1308157	0.1289347	0.0700857	0.1970343	0.0649260	0.6403657	1.5062114	4.626314	69.95743	0.0085898	0.0372216	0.0462445	0.0166229	0.0252451	0.0052977	18.44783	27.04571	123.17400	1155.2086	0.1350966	0.3186271	0.3576463	0.1426080	0.3080829	0.0917754	0.4624861	0.6535477
0.1033860	0.5708874	N47	47	0.0832546	0.4545349	NA	18230737.0	0.6285714	15.49009	20.75429	101.91514	804.6686	0.1006531	0.1308157	0.1289347	0.0700857	0.1970343	0.0649260	0.6403657	1.5062114	4.626314	69.95743	0.0085898	0.0372216	0.0462445	0.0166229	0.0252451	0.0052977	18.44783	27.04571	123.17400	1155.2086	0.1350966	0.3186271	0.3576463	0.1426080	0.3080829	0.0917754	0.4624861	0.6535477
0.1294149	0.8502782	N59	59	0.1737855	0.7702426	NA	859711.0	0.0000000	8.88800	14.64000	58.79000	244.0000	0.0978300	0.1531000	0.0860600	0.0287200	0.1902000	0.0898000	0.5262000	0.8522000	3.168000	25.44000	0.0172100	0.0936800	0.0567100	0.0176600	0.0254100	0.0219300	9.73300	15.67000	62.56000	284.4000	0.1207000	0.2436000	0.1434000	0.0478600	0.2254000	0.1084000	0.5919389	0.7977983
0.1689766	0.4723279	N43	43	0.1886496	0.3492252	NA	34306209.3	0.6538462	16.06606	21.74596	105.45250	862.2731	0.0971142	0.1237775	0.1221242	0.0682241	0.1872423	0.0626077	0.5695192	1.4395923	4.078096	61.13267	0.0072560	0.0320094	0.0372661	0.0137623	0.0221185	0.0043778	19.00894	28.60635	126.84442	1211.7596	0.1330125	0.3177973	0.3577069	0.1444533	0.2971288	0.0882800	0.4384754	0.5873970
0.1689766	0.4723279	N43	43	0.2881142	0.4237081	NA	34306209.3	0.6538462	16.06606	21.74596	105.45250	862.2731	0.0971142	0.1237775	0.1221242	0.0682241	0.1872423	0.0626077	0.5695192	1.4395923	4.078096	61.13267	0.0072560	0.0320094	0.0372661	0.0137623	0.0221185	0.0043778	19.00894	28.60635	126.84442	1211.7596	0.1330125	0.3177973	0.3577069	0.1444533	0.2971288	0.0882800	0.4384754	0.5873970
0.1701194	0.0892239	N68	68	0.2647630	0.0496826	NA	202786298.2	1.0000000	22.27600	21.85800	152.57600	1678.4200	0.1276800	0.2532800	0.3454400	0.1590400	0.2373400	0.0718220	1.6712600	1.7886000	12.506200	288.88600	0.0127840	0.0644900	0.0875900	0.0205740	0.0497700	0.0068208	25.69000	26.41000	177.95400	2203.3400	0.1586400	0.4968600	0.6077400	0.2310200	0.3917800	0.0964500	0.9224915	0.8633097
0.1701194	0.0892239	N68	68	0.2001185	0.0067192	NA	202786298.2	1.0000000	22.27600	21.85800	152.57600	1678.4200	0.1276800	0.2532800	0.3454400	0.1590400	0.2373400	0.0718220	1.6712600	1.7886000	12.506200	288.88600	0.0127840	0.0644900	0.0875900	0.0205740	0.0497700	0.0068208	25.69000	26.41000	177.95400	2203.3400	0.1586400	0.4968600	0.6077400	0.2310200	0.3917800	0.0964500	0.9224915	0.8633097
0.1701194	0.0892239	N68	68	0.1062707	0.1651024	NA	202786298.2	1.0000000	22.27600	21.85800	152.57600	1678.4200	0.1276800	0.2532800	0.3454400	0.1590400	0.2373400	0.0718220	1.6712600	1.7886000	12.506200	288.88600	0.0127840	0.0644900	0.0875900	0.0205740	0.0497700	0.0068208	25.69000	26.41000	177.95400	2203.3400	0.1586400	0.4968600	0.6077400	0.2310200	0.3917800	0.0964500	0.9224915	0.8633097
0.1737855	0.7702426	N54	54	0.1883090	0.6719276	NA	52980914.8	0.4736842	13.32274	20.61105	87.61211	607.8421	0.1013284	0.1457584	0.1384979	0.0649463	0.2029789	0.0720147	0.5896947	1.6380895	4.221474	55.77726	0.0098870	0.0506637	0.0610700	0.0193923	0.0274159	0.0078586	15.64616	26.18526	103.83263	880.1316	0.1320126	0.2966289	0.3258253	0.1261811	0.3029211	0.0962553	0.5532015	0.7321746
0.1737855	0.7702426	N54	54	0.0810987	0.6660942	NA	52980914.8	0.4736842	13.32274	20.61105	87.61211	607.8421	0.1013284	0.1457584	0.1384979	0.0649463	0.2029789	0.0720147	0.5896947	1.6380895	4.221474	55.77726	0.0098870	0.0506637	0.0610700	0.0193923	0.0274159	0.0078586	15.64616	26.18526	103.83263	880.1316	0.1320126	0.2966289	0.3258253	0.1261811	0.3029211	0.0962553	0.5532015	0.7321746
0.1883090	0.6719276	N48	48	0.2222091	0.5737410	NA	18064352.7	0.6250000	15.32775	21.80025	101.35600	804.7600	0.1007560	0.1472350	0.1566078	0.0769632	0.1951200	0.0673970	0.6180150	1.4266125	4.482450	69.79552	0.0081543	0.0395294	0.0500554	0.0154782	0.0233167	0.0058689	18.47563	28.10550	124.17650	1199.5025	0.1376388	0.3535958	0.4135202	0.1531428	0.3023725	0.0968892	0.5381257	0.6710598
0.1883090	0.6719276	N48	48	0.1033860	0.5708874	NA	18064352.7	0.6250000	15.32775	21.80025	101.35600	804.7600	0.1007560	0.1472350	0.1566078	0.0769632	0.1951200	0.0673970	0.6180150	1.4266125	4.482450	69.79552	0.0081543	0.0395294	0.0500554	0.0154782	0.0233167	0.0058689	18.47563	28.10550	124.17650	1199.5025	0.1376388	0.3535958	0.4135202	0.1531428	0.3023725	0.0968892	0.5381257	0.6710598
0.1886496	0.3492252	N42	42	0.3390217	0.3169053	NA	39713198.7	0.5616438	14.87360	20.94918	97.21534	727.2630	0.1007386	0.1137412	0.1108364	0.0610652	0.1863685	0.0632308	0.4827863	1.4852329	3.341548	47.77570	0.0084535	0.0281595	0.0358687	0.0136363	0.0227738	0.0042736	17.29012	27.63205	114.31767	992.0370	0.1379126	0.2613212	0.3075953	0.1255544	0.2884342	0.0843730	0.3550034	0.5691102
0.1886496	0.3492252	N42	42	0.2568029	0.2380713	NA	39713198.7	0.5616438	14.87360	20.94918	97.21534	727.2630	0.1007386	0.1137412	0.1108364	0.0610652	0.1863685	0.0632308	0.4827863	1.4852329	3.341548	47.77570	0.0084535	0.0281595	0.0358687	0.0136363	0.0227738	0.0042736	17.29012	27.63205	114.31767	992.0370	0.1379126	0.2613212	0.3075953	0.1255544	0.2884342	0.0843730	0.3550034	0.5691102
0.2016626	0.4678645	N38	38	0.2881142	0.4237081	NA	894335.0	0.0000000	12.43000	17.00000	78.60000	477.3000	0.0755700	0.0345400	0.0134200	0.0169900	0.1472000	0.0556100	0.3778000	2.2000000	2.487000	31.16000	0.0073570	0.0107900	0.0099590	0.0112000	0.0343300	0.0029610	12.90000	20.21000	81.76000	515.9000	0.0840900	0.0471200	0.0223700	0.0283200	0.1901000	0.0593200	0.4928099	0.5429805
0.2078948	0.9004729	N62	62	0.3057724	0.8561349	NA	859711.0	0.0000000	8.88800	14.64000	58.79000	244.0000	0.0978300	0.1531000	0.0860600	0.0287200	0.1902000	0.0898000	0.5262000	0.8522000	3.168000	25.44000	0.0172100	0.0936800	0.0567100	0.0176600	0.0254100	0.0219300	9.73300	15.67000	62.56000	284.4000	0.1207000	0.2436000	0.1434000	0.0478600	0.2254000	0.1084000	0.5919389	0.7977983
0.2078948	0.9004729	N62	62	0.1294149	0.8502782	NA	859711.0	0.0000000	8.88800	14.64000	58.79000	244.0000	0.0978300	0.1531000	0.0860600	0.0287200	0.1902000	0.0898000	0.5262000	0.8522000	3.168000	25.44000	0.0172100	0.0936800	0.0567100	0.0176600	0.0254100	0.0219300	9.73300	15.67000	62.56000	284.4000	0.1207000	0.2436000	0.1434000	0.0478600	0.2254000	0.1084000	0.5919389	0.7977983
0.2222091	0.5737410	N44	44	0.2016626	0.4678645	NA	19811714.6	0.6400000	15.76132	21.97520	104.32840	850.0120	0.0984096	0.1449108	0.1514876	0.0772068	0.1949880	0.0665340	0.6078200	1.3669880	4.576720	66.31288	0.0068069	0.0352177	0.0438014	0.0134861	0.0235224	0.0050477	18.80972	28.40880	128.24480	1213.3520	0.1325032	0.3728040	0.4403420	0.1531428	0.3124640	0.0969368	0.5219885	0.6073919
0.2222091	0.5737410	N44	44	0.2997246	0.5267026	NA	19811714.6	0.6400000	15.76132	21.97520	104.32840	850.0120	0.0984096	0.1449108	0.1514876	0.0772068	0.1949880	0.0665340	0.6078200	1.3669880	4.576720	66.31288	0.0068069	0.0352177	0.0438014	0.0134861	0.0235224	0.0050477	18.80972	28.40880	128.24480	1213.3520	0.1325032	0.3728040	0.4403420	0.1531428	0.3124640	0.0969368	0.5219885	0.6073919
0.2222091	0.5737410	N44	44	0.1689766	0.4723279	NA	19811714.6	0.6400000	15.76132	21.97520	104.32840	850.0120	0.0984096	0.1449108	0.1514876	0.0772068	0.1949880	0.0665340	0.6078200	1.3669880	4.576720	66.31288	0.0068069	0.0352177	0.0438014	0.0134861	0.0235224	0.0050477	18.80972	28.40880	128.24480	1213.3520	0.1325032	0.3728040	0.4403420	0.1531428	0.3124640	0.0969368	0.5219885	0.6073919
0.2568029	0.2380713	N41	41	0.3801900	0.1970649	NA	43317541.8	0.5862069	14.41610	21.15345	93.99345	675.4379	0.0986752	0.1086186	0.0938924	0.0536076	0.1801552	0.0615779	0.4449793	1.3587690	3.201448	42.32124	0.0085912	0.0269869	0.0353378	0.0148876	0.0209721	0.0036257	16.52083	27.11862	109.90207	894.4517	0.1359345	0.2504324	0.2792334	0.1234548	0.2757172	0.0801814	0.2883097	0.5477604
0.2881142	0.4237081	N36	36	0.4063064	0.4116395	NA	51669171.2	0.6000000	15.29480	20.95600	99.79520	793.9680	0.0943020	0.1046872	0.1063171	0.0608663	0.1821960	0.0612460	0.4642280	1.2885400	3.303120	50.57820	0.0063107	0.0235886	0.0294121	0.0111691	0.0206240	0.0033236	18.23476	27.96320	120.88000	1152.1560	0.1282120	0.2687320	0.3141836	0.1321000	0.2935680	0.0832208	0.4210566	0.5193592
0.2881142	0.4237081	N36	36	0.3390217	0.3169053	NA	51669171.2	0.6000000	15.29480	20.95600	99.79520	793.9680	0.0943020	0.1046872	0.1063171	0.0608663	0.1821960	0.0612460	0.4642280	1.2885400	3.303120	50.57820	0.0063107	0.0235886	0.0294121	0.0111691	0.0206240	0.0033236	18.23476	27.96320	120.88000	1152.1560	0.1282120	0.2687320	0.3141836	0.1321000	0.2935680	0.0832208	0.4210566	0.5193592
0.2997246	0.5267026	N37	37	0.2881142	0.4237081	NA	4551125.0	0.5000000	17.03000	22.31000	112.97500	964.9000	0.0878250	0.1513500	0.1621150	0.0899400	0.1513500	0.0639950	0.5637000	1.0669500	4.669500	69.87450	0.0045100	0.0369050	0.0394050	0.0156900	0.0199400	0.0055770	20.11500	27.25500	141.18000	1357.7000	0.1086950	0.3549500	0.3834000	0.1762000	0.2466000	0.0896150	0.5047916	0.5551850
0.3051285	0.7423285	N49	49	0.3069179	0.6516061	NA	15271760.3	0.8461538	17.99900	23.62385	120.38462	1100.2385	0.1091492	0.1871900	0.2156385	0.1084954	0.2081692	0.0692469	0.5882385	1.3847769	4.485769	76.60677	0.0075922	0.0406600	0.0514523	0.0158008	0.0219585	0.0053744	22.17631	33.09615	151.80923	1682.3692	0.1556308	0.5172900	0.5906846	0.2181923	0.3527000	0.1071808	0.6395179	0.6934180
0.3051285	0.7423285	N49	49	0.1883090	0.6719276	NA	15271760.3	0.8461538	17.99900	23.62385	120.38462	1100.2385	0.1091492	0.1871900	0.2156385	0.1084954	0.2081692	0.0692469	0.5882385	1.3847769	4.485769	76.60677	0.0075922	0.0406600	0.0514523	0.0158008	0.0219585	0.0053744	22.17631	33.09615	151.80923	1682.3692	0.1556308	0.5172900	0.5906846	0.2181923	0.3527000	0.1071808	0.6395179	0.6934180
0.3057724	0.8561349	N55	55	0.1737855	0.7702426	NA	12852619.8	0.5625000	14.68056	19.91187	98.36813	734.2313	0.1100681	0.1982731	0.1952350	0.0893375	0.2154000	0.0770612	0.5360250	1.3354625	3.893625	58.17175	0.0091695	0.0529875	0.0630375	0.0174625	0.0294800	0.0090179	17.69969	26.92625	120.78938	1121.9437	0.1482075	0.4655419	0.5132375	0.1763600	0.3518188	0.1120956	0.6488489	0.7413141
0.3057724	0.8561349	N55	55	0.3051285	0.7423285	NA	12852619.8	0.5625000	14.68056	19.91187	98.36813	734.2313	0.1100681	0.1982731	0.1952350	0.0893375	0.2154000	0.0770612	0.5360250	1.3354625	3.893625	58.17175	0.0091695	0.0529875	0.0630375	0.0174625	0.0294800	0.0090179	17.69969	26.92625	120.78938	1121.9437	0.1482075	0.4655419	0.5132375	0.1763600	0.3518188	0.1120956	0.6488489	0.7413141
0.3069179	0.6516061	N45	45	0.2222091	0.5737410	NA	84667401.0	1.0000000	13.73000	22.61000	93.60000	578.3000	0.1131000	0.2293000	0.2128000	0.0802500	0.2069000	0.0768200	0.2121000	1.1690000	2.061000	19.21000	0.0064290	0.0593600	0.0550100	0.0162800	0.0196100	0.0080930	15.03000	32.01000	108.80000	697.7000	0.1651000	0.7725000	0.6943000	0.2208000	0.3596000	0.1431000	0.5903791	0.6380966
0.3122399	0.9670893	N61	61	0.3057724	0.8561349	NA	485119202.0	0.5000000	15.91500	22.64500	105.26500	799.5000	0.0940850	0.1411000	0.1522000	0.0659950	0.1511000	0.0652900	0.7053500	1.7185000	4.063500	67.82000	0.0194460	0.0959750	0.1217000	0.0334900	0.0312600	0.0177100	16.92000	25.10000	111.05000	894.1500	0.1120650	0.2132500	0.2511500	0.1060000	0.1937500	0.0780850	0.6635286	0.8227825
0.3390217	0.3169053	N35	35	0.4932039	0.3547114	NA	32718713.7	0.6024096	15.27798	20.22325	99.77807	775.9434	0.0982083	0.1109277	0.1092437	0.0611492	0.1833108	0.0621029	0.4697386	1.2726578	3.193928	49.05439	0.0072157	0.0247359	0.0318245	0.0120915	0.0206929	0.0035904	17.99875	26.95313	118.43566	1090.2795	0.1364447	0.2726887	0.3158148	0.1319073	0.2953361	0.0847445	0.3409958	0.5096418
0.3390217	0.3169053	N35	35	0.3801900	0.1970649	NA	32718713.7	0.6024096	15.27798	20.22325	99.77807	775.9434	0.0982083	0.1109277	0.1092437	0.0611492	0.1833108	0.0621029	0.4697386	1.2726578	3.193928	49.05439	0.0072157	0.0247359	0.0318245	0.0120915	0.0206929	0.0035904	17.99875	26.95313	118.43566	1090.2795	0.1364447	0.2726887	0.3158148	0.1319073	0.2953361	0.0847445	0.3409958	0.5096418
0.3801900	0.1970649	N34	34	0.5133601	0.2209132	NA	10584515.0	0.4455446	13.99023	20.06644	91.23525	633.0941	0.0980265	0.1109529	0.0917531	0.0506595	0.1811634	0.0634276	0.3943634	1.2714248	2.824563	36.80066	0.0072961	0.0282688	0.0350737	0.0131708	0.0204602	0.0039207	16.07165	26.52277	106.30208	843.8059	0.1344217	0.2740756	0.2885514	0.1210808	0.2871802	0.0852774	0.2578535	0.4857521
0.3801900	0.1970649	N34	34	0.4347895	0.0860170	NA	10584515.0	0.4455446	13.99023	20.06644	91.23525	633.0941	0.0980265	0.1109529	0.0917531	0.0506595	0.1811634	0.0634276	0.3943634	1.2714248	2.824563	36.80066	0.0072961	0.0282688	0.0350737	0.0131708	0.0204602	0.0039207	16.07165	26.52277	106.30208	843.8059	0.1344217	0.2740756	0.2885514	0.1210808	0.2871802	0.0852774	0.2578535	0.4857521
0.3892211	0.8519800	N57	57	0.4232847	0.7851556	NA	8611555.0	1.0000000	25.22000	24.91000	171.50000	1878.0000	0.1063000	0.2665000	0.3339000	0.1845000	0.1829000	0.0678200	0.8973000	1.4740000	7.382000	120.00000	0.0081660	0.0569300	0.0573000	0.0203000	0.0106500	0.0058930	30.00000	33.62000	211.70000	2562.0000	0.1573000	0.6076000	0.6476000	0.2867000	0.2355000	0.1051000	0.7241484	0.7025255
0.3892211	0.8519800	N57	57	0.3057724	0.8561349	NA	8611555.0	1.0000000	25.22000	24.91000	171.50000	1878.0000	0.1063000	0.2665000	0.3339000	0.1845000	0.1829000	0.0678200	0.8973000	1.4740000	7.382000	120.00000	0.0081660	0.0569300	0.0573000	0.0203000	0.0106500	0.0058930	30.00000	33.62000	211.70000	2562.0000	0.1573000	0.6076000	0.6476000	0.2867000	0.2355000	0.1051000	0.7241484	0.7025255
0.4063064	0.4116395	N32	32	0.4932039	0.3547114	NA	911157302.0	1.0000000	21.10000	20.52000	138.10000	1384.0000	0.0968400	0.1175000	0.1572000	0.1155000	0.1554000	0.0566100	0.6643000	1.3610000	4.542000	81.89000	0.0054670	0.0207500	0.0318500	0.0146600	0.0102900	0.0022050	25.68000	32.07000	168.20000	2022.0000	0.1368000	0.3101000	0.4399000	0.2280000	0.2268000	0.0742500	0.3900611	0.4545824
0.4232847	0.7851556	N50	50	0.3051285	0.7423285	NA	6166328.7	1.0000000	19.13000	23.43667	129.16667	1183.5333	0.1140000	0.2550333	0.2505000	0.1325900	0.2140000	0.0737667	0.5795000	1.0879667	4.505000	71.81667	0.0066080	0.0500033	0.0473000	0.0164533	0.0153367	0.0052077	23.30667	33.30667	159.98667	1719.7000	0.1749333	0.7679667	0.7219333	0.2764667	0.3535667	0.1246000	0.7022116	0.7054340
0.4347895	0.0860170	N33	33	0.5528728	0.0907782	NA	15848615.5	0.4000000	14.21350	19.92450	92.29700	640.1650	0.0948765	0.1011755	0.0736000	0.0430940	0.1788700	0.0623210	0.3734000	1.2149100	2.617645	34.81400	0.0066280	0.0248040	0.0317900	0.0121240	0.0192105	0.0037842	16.26300	26.86100	106.70850	841.4550	0.1330650	0.2593640	0.2718400	0.1149160	0.2892950	0.0840550	0.1995680	0.4527368
0.4594123	0.8925995	N56	56	0.4882285	1.0000000	NA	8456946.7	0.8333333	16.75417	21.70083	113.40833	912.7417	0.1049900	0.2327783	0.2388667	0.1068642	0.2194667	0.0738367	0.6821583	1.9094250	5.626333	79.53083	0.0062604	0.0648680	0.0715117	0.0190058	0.0305158	0.0073741	20.43067	30.31667	142.73833	1363.8917	0.1438133	0.6594075	0.6793500	0.2141333	0.3799333	0.1194700	0.7254413	0.7622228
0.4594123	0.8925995	N56	56	0.4232847	0.7851556	NA	8456946.7	0.8333333	16.75417	21.70083	113.40833	912.7417	0.1049900	0.2327783	0.2388667	0.1068642	0.2194667	0.0738367	0.6821583	1.9094250	5.626333	79.53083	0.0062604	0.0648680	0.0715117	0.0190058	0.0305158	0.0073741	20.43067	30.31667	142.73833	1363.8917	0.1438133	0.6594075	0.6793500	0.2141333	0.3799333	0.1194700	0.7254413	0.7622228
0.4594123	0.8925995	N56	56	0.3057724	0.8561349	NA	8456946.7	0.8333333	16.75417	21.70083	113.40833	912.7417	0.1049900	0.2327783	0.2388667	0.1068642	0.2194667	0.0738367	0.6821583	1.9094250	5.626333	79.53083	0.0062604	0.0648680	0.0715117	0.0190058	0.0305158	0.0073741	20.43067	30.31667	142.73833	1363.8917	0.1438133	0.6594075	0.6793500	0.2141333	0.3799333	0.1194700	0.7254413	0.7622228
0.4932039	0.3547114	N31	31	0.5600864	0.3056733	NA	48838196.0	0.4761905	14.55952	17.41476	94.38714	712.8095	0.0917943	0.0894352	0.0827719	0.0482523	0.1681143	0.0607324	0.3646714	0.9813190	2.446619	37.47924	0.0061516	0.0190227	0.0242373	0.0094161	0.0170319	0.0028763	16.91024	23.68143	110.28476	968.0762	0.1308514	0.2357662	0.2647710	0.1175410	0.2725714	0.0808624	0.3199845	0.4335055
0.4932039	0.3547114	N31	31	0.6372009	0.4447802	NA	48838196.0	0.4761905	14.55952	17.41476	94.38714	712.8095	0.0917943	0.0894352	0.0827719	0.0482523	0.1681143	0.0607324	0.3646714	0.9813190	2.446619	37.47924	0.0061516	0.0190227	0.0242373	0.0094161	0.0170319	0.0028763	16.91024	23.68143	110.28476	968.0762	0.1308514	0.2357662	0.2647710	0.1175410	0.2725714	0.0808624	0.3199845	0.4335055
0.4932039	0.3547114	N31	31	0.5133601	0.2209132	NA	48838196.0	0.4761905	14.55952	17.41476	94.38714	712.8095	0.0917943	0.0894352	0.0827719	0.0482523	0.1681143	0.0607324	0.3646714	0.9813190	2.446619	37.47924	0.0061516	0.0190227	0.0242373	0.0094161	0.0170319	0.0028763	16.91024	23.68143	110.28476	968.0762	0.1308514	0.2357662	0.2647710	0.1175410	0.2725714	0.0808624	0.3199845	0.4335055
0.5133601	0.2209132	N30	30	0.5528728	0.0907782	NA	23476092.6	0.2989691	13.32347	18.62412	86.28619	570.2082	0.0958060	0.0950003	0.0686730	0.0395061	0.1766701	0.0631502	0.3213639	1.1464495	2.220632	28.60928	0.0068605	0.0223363	0.0279565	0.0106736	0.0191032	0.0035494	15.17131	25.12505	99.28021	745.4598	0.1351007	0.2409355	0.2449421	0.1061320	0.2883474	0.0851176	0.2321924	0.4164238
0.5133601	0.2209132	N30	30	0.6404168	0.2922932	NA	23476092.6	0.2989691	13.32347	18.62412	86.28619	570.2082	0.0958060	0.0950003	0.0686730	0.0395061	0.1766701	0.0631502	0.3213639	1.1464495	2.220632	28.60928	0.0068605	0.0223363	0.0279565	0.0106736	0.0191032	0.0035494	15.17131	25.12505	99.28021	745.4598	0.1351007	0.2409355	0.2449421	0.1061320	0.2883474	0.0851176	0.2321924	0.4164238
0.5528728	0.0907782	N29	29	0.6637661	0.1566513	NA	23575258.3	0.2631579	13.09599	18.66447	84.69105	543.5605	0.0963203	0.0922289	0.0608997	0.0355610	0.1736053	0.0629233	0.3082421	1.1933829	2.159472	25.90987	0.0069000	0.0220297	0.0271489	0.0106714	0.0187188	0.0034155	14.83895	25.81263	97.36355	701.4434	0.1364624	0.2384346	0.2360724	0.1040430	0.2854684	0.0846041	0.1828726	0.3972866
0.5528728	0.0907782	N29	29	0.6264635	0.0008187	NA	23575258.3	0.2631579	13.09599	18.66447	84.69105	543.5605	0.0963203	0.0922289	0.0608997	0.0355610	0.1736053	0.0629233	0.3082421	1.1933829	2.159472	25.90987	0.0069000	0.0220297	0.0271489	0.0106714	0.0187188	0.0034155	14.83895	25.81263	97.36355	701.4434	0.1364624	0.2384346	0.2360724	0.1040430	0.2854684	0.0846041	0.1828726	0.3972866
0.5528728	0.0907782	N29	29	0.5876230	0.0000000	NA	23575258.3	0.2631579	13.09599	18.66447	84.69105	543.5605	0.0963203	0.0922289	0.0608997	0.0355610	0.1736053	0.0629233	0.3082421	1.1933829	2.159472	25.90987	0.0069000	0.0220297	0.0271489	0.0106714	0.0187188	0.0034155	14.83895	25.81263	97.36355	701.4434	0.1364624	0.2384346	0.2360724	0.1040430	0.2854684	0.0846041	0.1828726	0.3972866
0.5569509	0.8466482	N64	64	0.4594123	0.8925995	NA	84501001.0	1.0000000	12.46000	24.04000	83.97000	475.9000	0.1186000	0.2396000	0.2273000	0.0854300	0.2030000	0.0824300	0.2976000	1.5990000	2.039000	23.94000	0.0071490	0.0721700	0.0774300	0.0143200	0.0178900	0.0100800	15.09000	40.68000	97.65000	711.4000	0.1853000	1.0580000	1.1050000	0.2210000	0.4366000	0.2075000	0.7271720	0.7927863
0.5600864	0.3056733	N22	22	0.6404168	0.2922932	NA	85638502.0	1.0000000	13.17000	21.81000	85.42000	531.5000	0.0971400	0.1047000	0.0825900	0.0525200	0.1746000	0.0617700	0.1938000	0.6123000	1.334000	14.49000	0.0033500	0.0138400	0.0145200	0.0068530	0.0111300	0.0017200	16.23000	29.89000	105.50000	740.7000	0.1503000	0.3904000	0.3728000	0.1607000	0.3693000	0.0961800	0.2951131	0.3821034
0.5727938	0.9560023	N63	63	0.4594123	0.8925995	NA	859045.0	0.7500000	15.37225	22.51500	103.46500	771.8500	0.1005775	0.2118500	0.2320750	0.0803350	0.2300500	0.0743275	0.6375000	2.1345000	5.974250	67.62250	0.0068015	0.1012575	0.1516325	0.0292900	0.0478175	0.0104412	17.77500	30.73500	125.25000	1017.5250	0.1324750	0.6259750	0.7972250	0.1945500	0.4310000	0.1170500	0.7326821	0.8170121
0.5727938	0.9560023	N63	63	0.6627955	0.9858353	NA	859045.0	0.7500000	15.37225	22.51500	103.46500	771.8500	0.1005775	0.2118500	0.2320750	0.0803350	0.2300500	0.0743275	0.6375000	2.1345000	5.974250	67.62250	0.0068015	0.1012575	0.1516325	0.0292900	0.0478175	0.0104412	17.77500	30.73500	125.25000	1017.5250	0.1324750	0.6259750	0.7972250	0.1945500	0.4310000	0.1170500	0.7326821	0.8170121
0.5876230	0.0000000	N28	28	0.6937162	0.0440214	NA	917896.0	0.0000000	13.71000	18.68000	88.73000	571.0000	0.0991600	0.1070000	0.0538500	0.0378300	0.1714000	0.0684300	0.3191000	1.2490000	2.284000	26.45000	0.0067390	0.0225100	0.0208600	0.0135200	0.0187000	0.0037470	15.11000	25.63000	99.43000	701.9000	0.1425000	0.2566000	0.1935000	0.1284000	0.2849000	0.0903100	0.0803571	0.3393867
0.6264635	0.0008187	N27	27	0.6937162	0.0440214	NA	8915.0	0.0000000	14.96000	19.10000	97.03000	687.3000	0.0899200	0.0982300	0.0594000	0.0481900	0.1879000	0.0585200	0.2877000	0.9480000	2.171000	24.87000	0.0053320	0.0211500	0.0153600	0.0118700	0.0152200	0.0028150	16.25000	26.19000	109.10000	809.8000	0.1313000	0.3030000	0.1804000	0.1489000	0.2962000	0.0847200	0.0921641	0.3549579
0.6372009	0.4447802	N23	23	0.6404168	0.2922932	NA	2401257.0	0.0000000	12.17700	15.87600	77.18900	462.8100	0.0803710	0.0390720	0.0085071	0.0080664	0.1560600	0.0570980	0.2719600	0.9711600	1.774100	21.31900	0.0057797	0.0074750	0.0054729	0.0047514	0.0176810	0.0019791	13.43000	20.29300	85.31000	562.9800	0.1070360	0.0755330	0.0375649	0.0331752	0.2344200	0.0667640	0.3199642	0.3000376
0.6372009	0.4447802	N23	23	0.7816898	0.4808277	NA	2401257.0	0.0000000	12.17700	15.87600	77.18900	462.8100	0.0803710	0.0390720	0.0085071	0.0080664	0.1560600	0.0570980	0.2719600	0.9711600	1.774100	21.31900	0.0057797	0.0074750	0.0054729	0.0047514	0.0176810	0.0019791	13.43000	20.29300	85.31000	562.9800	0.1070360	0.0755330	0.0375649	0.0331752	0.2344200	0.0667640	0.3199642	0.3000376
0.6404168	0.2922932	N21	21	0.6637661	0.1566513	NA	34593818.7	0.1250000	12.85481	17.66646	82.60250	517.4458	0.0907977	0.0751083	0.0422315	0.0272670	0.1680771	0.0609654	0.2418229	0.9699083	1.699417	19.40594	0.0061848	0.0154045	0.0174511	0.0078542	0.0183419	0.0026642	14.37175	23.55625	93.41771	644.4625	0.1277833	0.1918925	0.1722505	0.0826352	0.2834938	0.0797235	0.2257065	0.3284520
0.6404168	0.2922932	N21	21	0.7737367	0.3426981	NA	34593818.7	0.1250000	12.85481	17.66646	82.60250	517.4458	0.0907977	0.0751083	0.0422315	0.0272670	0.1680771	0.0609654	0.2418229	0.9699083	1.699417	19.40594	0.0061848	0.0154045	0.0174511	0.0078542	0.0183419	0.0026642	14.37175	23.55625	93.41771	644.4625	0.1277833	0.1918925	0.1722505	0.0826352	0.2834938	0.0797235	0.2257065	0.3284520
0.6637661	0.1566513	N20	20	0.7810610	0.2102647	NA	21294574.7	0.1165049	12.99165	18.01476	83.69204	527.2563	0.0947325	0.0825879	0.0471783	0.0308332	0.1734204	0.0611190	0.2742350	1.0669806	1.922990	22.12650	0.0062665	0.0172985	0.0203671	0.0092054	0.0183719	0.0026930	14.58728	24.39437	95.05524	662.9670	0.1310534	0.1985305	0.1853923	0.0912937	0.2827408	0.0786179	0.1542181	0.3114902
0.6637661	0.1566513	N20	20	0.6937162	0.0440214	NA	21294574.7	0.1165049	12.99165	18.01476	83.69204	527.2563	0.0947325	0.0825879	0.0471783	0.0308332	0.1734204	0.0611190	0.2742350	1.0669806	1.922990	22.12650	0.0062665	0.0172985	0.0203671	0.0092054	0.0183719	0.0026930	14.58728	24.39437	95.05524	662.9670	0.1310534	0.1985305	0.1853923	0.0912937	0.2827408	0.0786179	0.1542181	0.3114902
0.6795823	0.7156332	N26	26	0.7409975	0.7920048	NA	893526.0	0.0000000	13.50000	12.71000	85.69000	566.2000	0.0737600	0.0361400	0.0027580	0.0044190	0.1365000	0.0533500	0.2244000	0.6864000	1.509000	20.39000	0.0033380	0.0037460	0.0020300	0.0032420	0.0148000	0.0015660	14.97000	16.94000	95.48000	698.7000	0.0902300	0.0583600	0.0137900	0.0221000	0.2267000	0.0619200	0.5103685	0.2737304
0.6795823	0.7156332	N26	26	0.6952197	0.5985622	NA	893526.0	0.0000000	13.50000	12.71000	85.69000	566.2000	0.0737600	0.0361400	0.0027580	0.0044190	0.1365000	0.0533500	0.2244000	0.6864000	1.509000	20.39000	0.0033380	0.0037460	0.0020300	0.0032420	0.0148000	0.0015660	14.97000	16.94000	95.48000	698.7000	0.0902300	0.0583600	0.0137900	0.0221000	0.2267000	0.0619200	0.5103685	0.2737304
0.6937162	0.0440214	N19	19	0.7974626	0.0958983	NA	12220306.6	0.0384615	12.94154	18.13423	83.26269	521.7000	0.0916535	0.0778862	0.0422423	0.0279635	0.1766923	0.0603042	0.2882154	1.0892192	2.019192	22.68846	0.0063235	0.0181152	0.0202201	0.0091206	0.0177715	0.0027689	14.42692	24.62962	93.95808	643.1538	0.1284692	0.1907531	0.1674554	0.0858404	0.2783038	0.0772723	0.1095540	0.2872277
0.6952197	0.5985622	N24	24	0.8090653	0.6001076	NA	300940639.0	0.0000000	12.84333	15.87667	81.43333	513.2333	0.0777433	0.0336600	0.0028083	0.0054303	0.1369333	0.0539767	0.2490333	0.7847333	1.628333	20.46000	0.0046830	0.0038170	0.0018143	0.0034163	0.0163867	0.0013227	14.01000	19.21000	88.92667	609.5333	0.0978533	0.0503867	0.0122503	0.0220967	0.2139000	0.0596233	0.4474120	0.2807929
0.6952197	0.5985622	N24	24	0.7557747	0.7049098	NA	300940639.0	0.0000000	12.84333	15.87667	81.43333	513.2333	0.0777433	0.0336600	0.0028083	0.0054303	0.1369333	0.0539767	0.2490333	0.7847333	1.628333	20.46000	0.0046830	0.0038170	0.0018143	0.0034163	0.0163867	0.0013227	14.01000	19.21000	88.92667	609.5333	0.0978533	0.0503867	0.0122503	0.0220967	0.2139000	0.0596233	0.4474120	0.2807929
0.6952197	0.5985622	N24	24	0.6372009	0.4447802	NA	300940639.0	0.0000000	12.84333	15.87667	81.43333	513.2333	0.0777433	0.0336600	0.0028083	0.0054303	0.1369333	0.0539767	0.2490333	0.7847333	1.628333	20.46000	0.0046830	0.0038170	0.0018143	0.0034163	0.0163867	0.0013227	14.01000	19.21000	88.92667	609.5333	0.0978533	0.0503867	0.0122503	0.0220967	0.2139000	0.0596233	0.4474120	0.2807929
0.7409975	0.7920048	N18	18	0.7557747	0.7049098	NA	893526.0	0.0000000	13.50000	12.71000	85.69000	566.2000	0.0737600	0.0361400	0.0027580	0.0044190	0.1365000	0.0533500	0.2244000	0.6864000	1.509000	20.39000	0.0033380	0.0037460	0.0020300	0.0032420	0.0148000	0.0015660	14.97000	16.94000	95.48000	698.7000	0.0902300	0.0583600	0.0137900	0.0221000	0.2267000	0.0619200	0.5103685	0.2737304
0.7737367	0.3426981	N14	14	0.8982205	0.3966470	NA	46431064.8	0.1612903	13.50968	17.70032	86.64387	576.9774	0.0853723	0.0648603	0.0372676	0.0259161	0.1621323	0.0580371	0.2428516	0.8659484	1.652807	21.17916	0.0052847	0.0116236	0.0120180	0.0068389	0.0156152	0.0019801	15.07290	23.43323	97.26742	720.0581	0.1184558	0.1589381	0.1385448	0.0754433	0.2640968	0.0724403	0.2309404	0.2269114
0.7737367	0.3426981	N14	14	0.7810610	0.2102647	NA	46431064.8	0.1612903	13.50968	17.70032	86.64387	576.9774	0.0853723	0.0648603	0.0372676	0.0259161	0.1621323	0.0580371	0.2428516	0.8659484	1.652807	21.17916	0.0052847	0.0116236	0.0120180	0.0068389	0.0156152	0.0019801	15.07290	23.43323	97.26742	720.0581	0.1184558	0.1589381	0.1385448	0.0754433	0.2640968	0.0724403	0.2309404	0.2269114
0.7810610	0.2102647	N13	13	0.8887602	0.2670623	NA	36263634.7	0.0886076	12.95823	17.58076	83.16608	524.2937	0.0914839	0.0711961	0.0379083	0.0270009	0.1700114	0.0593785	0.2602152	1.0086608	1.779739	21.04470	0.0059978	0.0134638	0.0160586	0.0082625	0.0173881	0.0022133	14.44405	23.77443	93.48329	649.4253	0.1261225	0.1619176	0.1499967	0.0798890	0.2730544	0.0734968	0.1429412	0.2369588
0.7810610	0.2102647	N13	13	0.7974626	0.0958983	NA	36263634.7	0.0886076	12.95823	17.58076	83.16608	524.2937	0.0914839	0.0711961	0.0379083	0.0270009	0.1700114	0.0593785	0.2602152	1.0086608	1.779739	21.04470	0.0059978	0.0134638	0.0160586	0.0082625	0.0173881	0.0022133	14.44405	23.77443	93.48329	649.4253	0.1261225	0.1619176	0.1499967	0.0798890	0.2730544	0.0734968	0.1429412	0.2369588
0.7816898	0.4808277	N15	15	0.8955078	0.5275841	NA	8865563.7	0.0000000	13.00500	16.16833	82.59167	527.4000	0.0768517	0.0417425	0.0097398	0.0084916	0.1610917	0.0565292	0.2551000	0.8074750	1.689333	20.90550	0.0046974	0.0083318	0.0060960	0.0045044	0.0165725	0.0019592	14.30667	20.77083	91.53167	639.3417	0.1013942	0.1017175	0.0515155	0.0373127	0.2516000	0.0690992	0.3175273	0.2309455
0.7816898	0.4808277	N15	15	0.8860164	0.4792898	NA	8865563.7	0.0000000	13.00500	16.16833	82.59167	527.4000	0.0768517	0.0417425	0.0097398	0.0084916	0.1610917	0.0565292	0.2551000	0.8074750	1.689333	20.90550	0.0046974	0.0083318	0.0060960	0.0045044	0.0165725	0.0019592	14.30667	20.77083	91.53167	639.3417	0.1013942	0.1017175	0.0515155	0.0373127	0.2516000	0.0690992	0.3175273	0.2309455
0.7816898	0.4808277	N15	15	0.7737367	0.3426981	NA	8865563.7	0.0000000	13.00500	16.16833	82.59167	527.4000	0.0768517	0.0417425	0.0097398	0.0084916	0.1610917	0.0565292	0.2551000	0.8074750	1.689333	20.90550	0.0046974	0.0083318	0.0060960	0.0045044	0.0165725	0.0019592	14.30667	20.77083	91.53167	639.3417	0.1013942	0.1017175	0.0515155	0.0373127	0.2516000	0.0690992	0.3175273	0.2309455
0.7974626	0.0958983	N12	12	0.8883941	0.1515406	NA	31496979.4	0.0250000	12.60800	17.92875	80.89525	493.2475	0.0931920	0.0727008	0.0377065	0.0258527	0.1766000	0.0597210	0.2626525	1.0906800	1.773725	20.53275	0.0061726	0.0143101	0.0171576	0.0082260	0.0184392	0.0022212	14.02850	24.62400	90.63825	606.9025	0.1291025	0.1643668	0.1526920	0.0784392	0.2844425	0.0737380	0.0982323	0.2246358
0.8090653	0.6001076	N16	16	0.9114649	0.6287522	NA	450968639.0	0.0000000	13.21000	17.11500	83.89500	544.2500	0.0723100	0.0374050	0.0108220	0.0069780	0.1567500	0.0532950	0.3026000	0.7872500	2.019000	25.71000	0.0047555	0.0094215	0.0103364	0.0053165	0.0184500	0.0015140	14.61500	20.47500	93.24000	665.5000	0.0888850	0.0832850	0.0563405	0.0308600	0.2387500	0.0607200	0.4155237	0.2171553
0.8090653	0.6001076	N16	16	0.7816898	0.4808277	NA	450968639.0	0.0000000	13.21000	17.11500	83.89500	544.2500	0.0723100	0.0374050	0.0108220	0.0069780	0.1567500	0.0532950	0.3026000	0.7872500	2.019000	25.71000	0.0047555	0.0094215	0.0103364	0.0053165	0.0184500	0.0015140	14.61500	20.47500	93.24000	665.5000	0.0888850	0.0832850	0.0563405	0.0308600	0.2387500	0.0607200	0.4155237	0.2171553
0.8439500	0.9272829	N40	40	0.8978652	0.8761455	NA	873357.0	0.0000000	13.01000	22.22000	82.01000	526.4000	0.0625100	0.0193800	0.0015950	0.0018520	0.1395000	0.0523400	0.1731000	1.1420000	1.101000	14.34000	0.0034180	0.0022520	0.0015950	0.0018520	0.0161300	0.0009683	14.00000	29.02000	88.18000	608.8000	0.0812500	0.0343200	0.0079770	0.0092590	0.2295000	0.0584300	0.6760216	0.4745825
0.8860164	0.4792898	N10	10	0.8982205	0.3966470	NA	892214.0	0.0000000	14.26000	18.17000	91.22000	633.1000	0.0657600	0.0522000	0.0247500	0.0137400	0.1635000	0.0558600	0.2300000	0.6690000	1.661000	20.56000	0.0031690	0.0137700	0.0107900	0.0052430	0.0110300	0.0019570	16.22000	25.26000	105.80000	819.7000	0.0944500	0.2167000	0.1565000	0.0753000	0.2636000	0.0767600	0.2990295	0.1909138
0.8883941	0.1515406	N6	6	0.9723289	0.2069405	NA	43875459.7	0.0000000	12.62077	17.10962	80.80115	491.9846	0.0919185	0.0689262	0.0333100	0.0243426	0.1680423	0.0597892	0.2356538	0.9716115	1.588731	18.41385	0.0058911	0.0136600	0.0158771	0.0081192	0.0175900	0.0020937	13.91385	23.25615	89.69962	595.2500	0.1277577	0.1608500	0.1423777	0.0801415	0.2750115	0.0735488	0.0837656	0.1465538
0.8887602	0.2670623	N7	7	0.9785210	0.2825671	NA	37852336.9	0.1428571	13.47171	16.84257	86.65286	567.8829	0.0920931	0.0760809	0.0440333	0.0318782	0.1668143	0.0594089	0.2569657	0.8378629	1.768626	21.80420	0.0055898	0.0134424	0.0157023	0.0086368	0.0163043	0.0021842	15.05714	22.51343	97.74486	708.4286	0.1268226	0.1776760	0.1671097	0.0931451	0.2750771	0.0750157	0.1379912	0.1505442
0.8887602	0.2670623	N7	7	0.9894057	0.3204815	NA	37852336.9	0.1428571	13.47171	16.84257	86.65286	567.8829	0.0920931	0.0760809	0.0440333	0.0318782	0.1668143	0.0594089	0.2569657	0.8378629	1.768626	21.80420	0.0055898	0.0134424	0.0157023	0.0086368	0.0163043	0.0021842	15.05714	22.51343	97.74486	708.4286	0.1268226	0.1776760	0.1671097	0.0931451	0.2750771	0.0750157	0.1379912	0.1505442
0.8887602	0.2670623	N7	7	0.8883941	0.1515406	NA	37852336.9	0.1428571	13.47171	16.84257	86.65286	567.8829	0.0920931	0.0760809	0.0440333	0.0318782	0.1668143	0.0594089	0.2569657	0.8378629	1.768626	21.80420	0.0055898	0.0134424	0.0157023	0.0086368	0.0163043	0.0021842	15.05714	22.51343	97.74486	708.4286	0.1268226	0.1776760	0.1671097	0.0931451	0.2750771	0.0750157	0.1379912	0.1505442
0.8955078	0.5275841	N9	9	0.8982205	0.3966470	NA	496160.0	0.0000000	13.54000	15.99000	86.22000	566.9500	0.0776850	0.0504100	0.0109555	0.0058840	0.1619500	0.0568400	0.2222000	0.5976500	1.456500	19.31000	0.0036800	0.0110055	0.0105040	0.0047010	0.0149550	0.0022775	14.96000	20.21000	95.83000	691.1000	0.0988200	0.1289500	0.0601500	0.0351850	0.2596500	0.0750400	0.3388907	0.1701202
0.8982205	0.3966470	N8	8	0.9975296	0.3776708	NA	8338244.9	0.5333333	15.72200	18.40067	101.79200	784.8600	0.0911880	0.0884140	0.0778871	0.0498181	0.1711600	0.0575600	0.3511800	0.8106733	2.396893	35.73313	0.0051771	0.0146744	0.0191307	0.0092052	0.0145260	0.0021651	18.41800	24.64000	120.03000	1074.6200	0.1285287	0.2204687	0.2554633	0.1224507	0.2818600	0.0761700	0.2320213	0.1588000
0.8982205	0.3966470	N8	8	1.0000000	0.4321081	NA	8338244.9	0.5333333	15.72200	18.40067	101.79200	784.8600	0.0911880	0.0884140	0.0778871	0.0498181	0.1711600	0.0575600	0.3511800	0.8106733	2.396893	35.73313	0.0051771	0.0146744	0.0191307	0.0092052	0.0145260	0.0021651	18.41800	24.64000	120.03000	1074.6200	0.1285287	0.2204687	0.2554633	0.1224507	0.2818600	0.0761700	0.2320213	0.1588000
0.8982205	0.3966470	N8	8	0.8887602	0.2670623	NA	8338244.9	0.5333333	15.72200	18.40067	101.79200	784.8600	0.0911880	0.0884140	0.0778871	0.0498181	0.1711600	0.0575600	0.3511800	0.8106733	2.396893	35.73313	0.0051771	0.0146744	0.0191307	0.0092052	0.0145260	0.0021651	18.41800	24.64000	120.03000	1074.6200	0.1285287	0.2204687	0.2554633	0.1224507	0.2818600	0.0761700	0.2320213	0.1588000
0.9114649	0.6287522	N11	11	0.8955078	0.5275841	NA	902976.0	0.0000000	13.88000	16.16000	88.37000	596.6000	0.0702600	0.0483100	0.0204500	0.0085070	0.1607000	0.0547400	0.2541000	0.6218000	1.709000	23.12000	0.0037280	0.0141500	0.0198800	0.0070160	0.0164700	0.0019700	15.51000	19.97000	99.66000	745.3000	0.0848400	0.1233000	0.1091000	0.0453700	0.2542000	0.0662300	0.3976192	0.1727545
0.9785210	0.2825671	N2	2	0.9723289	0.2069405	NA	2926816.8	0.2500000	14.65750	16.80250	94.50250	681.6750	0.0921300	0.0762275	0.0579725	0.0394100	0.1668250	0.0581300	0.2970750	0.7329250	1.759250	29.43750	0.0054635	0.0144272	0.0166480	0.0076245	0.0146650	0.0023742	16.51000	21.71250	105.58500	866.7000	0.1299500	0.1748500	0.1801650	0.0927075	0.2713500	0.0754250	0.1270697	0.0710288
0.9894057	0.3204815	N3	3	0.9723289	0.2069405	NA	2329930.0	0.3000000	14.64500	17.24900	94.45500	681.3500	0.0898260	0.0760020	0.0557820	0.0381800	0.1683300	0.0575730	0.2691200	0.7321100	1.825400	26.33500	0.0045897	0.0126788	0.0165827	0.0084750	0.0140920	0.0020668	16.81400	23.04600	109.13000	905.3800	0.1248210	0.1887400	0.2135450	0.1120090	0.2745500	0.0756330	0.1510884	0.0661011
0.9975296	0.3776708	N4	4	0.9785210	0.2825671	NA	908929.7	0.6666667	17.11333	18.05000	111.38667	919.9000	0.0963267	0.0955533	0.1013533	0.0664733	0.1775333	0.0565100	0.3890667	0.6986667	2.480667	45.66000	0.0059017	0.0157767	0.0226767	0.0108167	0.0147133	0.0023183	19.77000	22.92667	128.26667	1246.0667	0.1355000	0.2103333	0.2904333	0.1360500	0.2740000	0.0740100	0.1987076	0.0504876
0.9975296	0.3776708	N4	4	0.9894057	0.3204815	NA	908929.7	0.6666667	17.11333	18.05000	111.38667	919.9000	0.0963267	0.0955533	0.1013533	0.0664733	0.1775333	0.0565100	0.3890667	0.6986667	2.480667	45.66000	0.0059017	0.0157767	0.0226767	0.0108167	0.0147133	0.0023183	19.77000	22.92667	128.26667	1246.0667	0.1355000	0.2103333	0.2904333	0.1360500	0.2740000	0.0740100	0.1987076	0.0504876
1.0000000	0.4321081	N5	5	0.9894057	0.3204815	NA	4878079.5	0.5000000	15.92000	18.91000	102.92000	806.1500	0.0870550	0.0747600	0.0663350	0.0431900	0.1683500	0.0563100	0.3523500	0.9696000	2.431500	38.06500	0.0040275	0.0095470	0.0165950	0.0077170	0.0135650	0.0016525	19.19000	26.88000	126.05500	1172.5500	0.1246000	0.1669100	0.2422000	0.1225250	0.2699000	0.0731550	0.2191234	0.0397457
0.9723289	0.2069405	N1	1	0.9723289	0.2069405	NA	10567742.9	0.0000000	12.62000	16.54429	80.78214	492.4429	0.0894364	0.0667200	0.0298579	0.0204029	0.1678643	0.0593157	0.2257929	0.8187643	1.525714	17.30286	0.0051496	0.0140869	0.0156685	0.0069016	0.0155293	0.0022713	14.10071	22.27357	90.83786	610.5571	0.1245143	0.1752286	0.1510507	0.0769236	0.2771143	0.0760879	0.0731864	0.0522346
0.9785210	0.2825671	N2	2	0.9785210	0.2825671	NA	2926816.8	0.2500000	14.65750	16.80250	94.50250	681.6750	0.0921300	0.0762275	0.0579725	0.0394100	0.1668250	0.0581300	0.2970750	0.7329250	1.759250	29.43750	0.0054635	0.0144272	0.0166480	0.0076245	0.0146650	0.0023742	16.51000	21.71250	105.58500	866.7000	0.1299500	0.1748500	0.1801650	0.0927075	0.2713500	0.0754250	0.1270697	0.0710288
0.9894057	0.3204815	N3	3	0.9894057	0.3204815	NA	2329930.0	0.3000000	14.64500	17.24900	94.45500	681.3500	0.0898260	0.0760020	0.0557820	0.0381800	0.1683300	0.0575730	0.2691200	0.7321100	1.825400	26.33500	0.0045897	0.0126788	0.0165827	0.0084750	0.0140920	0.0020668	16.81400	23.04600	109.13000	905.3800	0.1248210	0.1887400	0.2135450	0.1120090	0.2745500	0.0756330	0.1510884	0.0661011
0.9975296	0.3776708	N4	4	0.9975296	0.3776708	NA	908929.7	0.6666667	17.11333	18.05000	111.38667	919.9000	0.0963267	0.0955533	0.1013533	0.0664733	0.1775333	0.0565100	0.3890667	0.6986667	2.480667	45.66000	0.0059017	0.0157767	0.0226767	0.0108167	0.0147133	0.0023183	19.77000	22.92667	128.26667	1246.0667	0.1355000	0.2103333	0.2904333	0.1360500	0.2740000	0.0740100	0.1987076	0.0504876
1.0000000	0.4321081	N5	5	1.0000000	0.4321081	NA	4878079.5	0.5000000	15.92000	18.91000	102.92000	806.1500	0.0870550	0.0747600	0.0663350	0.0431900	0.1683500	0.0563100	0.3523500	0.9696000	2.431500	38.06500	0.0040275	0.0095470	0.0165950	0.0077170	0.0135650	0.0016525	19.19000	26.88000	126.05500	1172.5500	0.1246000	0.1669100	0.2422000	0.1225250	0.2699000	0.0731550	0.2191234	0.0397457
0.8883941	0.1515406	N6	6	0.8883941	0.1515406	NA	43875459.7	0.0000000	12.62077	17.10962	80.80115	491.9846	0.0919185	0.0689262	0.0333100	0.0243426	0.1680423	0.0597892	0.2356538	0.9716115	1.588731	18.41385	0.0058911	0.0136600	0.0158771	0.0081192	0.0175900	0.0020937	13.91385	23.25615	89.69962	595.2500	0.1277577	0.1608500	0.1423777	0.0801415	0.2750115	0.0735488	0.0837656	0.1465538
0.8887602	0.2670623	N7	7	0.8887602	0.2670623	NA	37852336.9	0.1428571	13.47171	16.84257	86.65286	567.8829	0.0920931	0.0760809	0.0440333	0.0318782	0.1668143	0.0594089	0.2569657	0.8378629	1.768626	21.80420	0.0055898	0.0134424	0.0157023	0.0086368	0.0163043	0.0021842	15.05714	22.51343	97.74486	708.4286	0.1268226	0.1776760	0.1671097	0.0931451	0.2750771	0.0750157	0.1379912	0.1505442
0.8982205	0.3966470	N8	8	0.8982205	0.3966470	NA	8338244.9	0.5333333	15.72200	18.40067	101.79200	784.8600	0.0911880	0.0884140	0.0778871	0.0498181	0.1711600	0.0575600	0.3511800	0.8106733	2.396893	35.73313	0.0051771	0.0146744	0.0191307	0.0092052	0.0145260	0.0021651	18.41800	24.64000	120.03000	1074.6200	0.1285287	0.2204687	0.2554633	0.1224507	0.2818600	0.0761700	0.2320213	0.1588000
0.8955078	0.5275841	N9	9	0.8955078	0.5275841	NA	496160.0	0.0000000	13.54000	15.99000	86.22000	566.9500	0.0776850	0.0504100	0.0109555	0.0058840	0.1619500	0.0568400	0.2222000	0.5976500	1.456500	19.31000	0.0036800	0.0110055	0.0105040	0.0047010	0.0149550	0.0022775	14.96000	20.21000	95.83000	691.1000	0.0988200	0.1289500	0.0601500	0.0351850	0.2596500	0.0750400	0.3388907	0.1701202
0.8860164	0.4792898	N10	10	0.8860164	0.4792898	NA	892214.0	0.0000000	14.26000	18.17000	91.22000	633.1000	0.0657600	0.0522000	0.0247500	0.0137400	0.1635000	0.0558600	0.2300000	0.6690000	1.661000	20.56000	0.0031690	0.0137700	0.0107900	0.0052430	0.0110300	0.0019570	16.22000	25.26000	105.80000	819.7000	0.0944500	0.2167000	0.1565000	0.0753000	0.2636000	0.0767600	0.2990295	0.1909138
0.9114649	0.6287522	N11	11	0.9114649	0.6287522	NA	902976.0	0.0000000	13.88000	16.16000	88.37000	596.6000	0.0702600	0.0483100	0.0204500	0.0085070	0.1607000	0.0547400	0.2541000	0.6218000	1.709000	23.12000	0.0037280	0.0141500	0.0198800	0.0070160	0.0164700	0.0019700	15.51000	19.97000	99.66000	745.3000	0.0848400	0.1233000	0.1091000	0.0453700	0.2542000	0.0662300	0.3976192	0.1727545
0.7974626	0.0958983	N12	12	0.7974626	0.0958983	NA	31496979.4	0.0250000	12.60800	17.92875	80.89525	493.2475	0.0931920	0.0727008	0.0377065	0.0258527	0.1766000	0.0597210	0.2626525	1.0906800	1.773725	20.53275	0.0061726	0.0143101	0.0171576	0.0082260	0.0184392	0.0022212	14.02850	24.62400	90.63825	606.9025	0.1291025	0.1643668	0.1526920	0.0784392	0.2844425	0.0737380	0.0982323	0.2246358
0.7810610	0.2102647	N13	13	0.7810610	0.2102647	NA	36263634.7	0.0886076	12.95823	17.58076	83.16608	524.2937	0.0914839	0.0711961	0.0379083	0.0270009	0.1700114	0.0593785	0.2602152	1.0086608	1.779739	21.04470	0.0059978	0.0134638	0.0160586	0.0082625	0.0173881	0.0022133	14.44405	23.77443	93.48329	649.4253	0.1261225	0.1619176	0.1499967	0.0798890	0.2730544	0.0734968	0.1429412	0.2369588
0.7737367	0.3426981	N14	14	0.7737367	0.3426981	NA	46431064.8	0.1612903	13.50968	17.70032	86.64387	576.9774	0.0853723	0.0648603	0.0372676	0.0259161	0.1621323	0.0580371	0.2428516	0.8659484	1.652807	21.17916	0.0052847	0.0116236	0.0120180	0.0068389	0.0156152	0.0019801	15.07290	23.43323	97.26742	720.0581	0.1184558	0.1589381	0.1385448	0.0754433	0.2640968	0.0724403	0.2309404	0.2269114
0.7816898	0.4808277	N15	15	0.7816898	0.4808277	NA	8865563.7	0.0000000	13.00500	16.16833	82.59167	527.4000	0.0768517	0.0417425	0.0097398	0.0084916	0.1610917	0.0565292	0.2551000	0.8074750	1.689333	20.90550	0.0046974	0.0083318	0.0060960	0.0045044	0.0165725	0.0019592	14.30667	20.77083	91.53167	639.3417	0.1013942	0.1017175	0.0515155	0.0373127	0.2516000	0.0690992	0.3175273	0.2309455
0.8090653	0.6001076	N16	16	0.8090653	0.6001076	NA	450968639.0	0.0000000	13.21000	17.11500	83.89500	544.2500	0.0723100	0.0374050	0.0108220	0.0069780	0.1567500	0.0532950	0.3026000	0.7872500	2.019000	25.71000	0.0047555	0.0094215	0.0103364	0.0053165	0.0184500	0.0015140	14.61500	20.47500	93.24000	665.5000	0.0888850	0.0832850	0.0563405	0.0308600	0.2387500	0.0607200	0.4155237	0.2171553
0.7557747	0.7049098	N17	17	0.7557747	0.7049098	NA	893526.0	0.0000000	13.50000	12.71000	85.69000	566.2000	0.0737600	0.0361400	0.0027580	0.0044190	0.1365000	0.0533500	0.2244000	0.6864000	1.509000	20.39000	0.0033380	0.0037460	0.0020300	0.0032420	0.0148000	0.0015660	14.97000	16.94000	95.48000	698.7000	0.0902300	0.0583600	0.0137900	0.0221000	0.2267000	0.0619200	0.5103685	0.2737304
0.7409975	0.7920048	N18	18	0.7409975	0.7920048	NA	893526.0	0.0000000	13.50000	12.71000	85.69000	566.2000	0.0737600	0.0361400	0.0027580	0.0044190	0.1365000	0.0533500	0.2244000	0.6864000	1.509000	20.39000	0.0033380	0.0037460	0.0020300	0.0032420	0.0148000	0.0015660	14.97000	16.94000	95.48000	698.7000	0.0902300	0.0583600	0.0137900	0.0221000	0.2267000	0.0619200	0.5103685	0.2737304
0.6937162	0.0440214	N19	19	0.6937162	0.0440214	NA	12220306.6	0.0384615	12.94154	18.13423	83.26269	521.7000	0.0916535	0.0778862	0.0422423	0.0279635	0.1766923	0.0603042	0.2882154	1.0892192	2.019192	22.68846	0.0063235	0.0181152	0.0202201	0.0091206	0.0177715	0.0027689	14.42692	24.62962	93.95808	643.1538	0.1284692	0.1907531	0.1674554	0.0858404	0.2783038	0.0772723	0.1095540	0.2872277
0.6637661	0.1566513	N20	20	0.6637661	0.1566513	NA	21294574.7	0.1165049	12.99165	18.01476	83.69204	527.2563	0.0947325	0.0825879	0.0471783	0.0308332	0.1734204	0.0611190	0.2742350	1.0669806	1.922990	22.12650	0.0062665	0.0172985	0.0203671	0.0092054	0.0183719	0.0026930	14.58728	24.39437	95.05524	662.9670	0.1310534	0.1985305	0.1853923	0.0912937	0.2827408	0.0786179	0.1542181	0.3114902
0.6404168	0.2922932	N21	21	0.6404168	0.2922932	NA	34593818.7	0.1250000	12.85481	17.66646	82.60250	517.4458	0.0907977	0.0751083	0.0422315	0.0272670	0.1680771	0.0609654	0.2418229	0.9699083	1.699417	19.40594	0.0061848	0.0154045	0.0174511	0.0078542	0.0183419	0.0026642	14.37175	23.55625	93.41771	644.4625	0.1277833	0.1918925	0.1722505	0.0826352	0.2834938	0.0797235	0.2257065	0.3284520
0.5600864	0.3056733	N22	22	0.5600864	0.3056733	NA	85638502.0	1.0000000	13.17000	21.81000	85.42000	531.5000	0.0971400	0.1047000	0.0825900	0.0525200	0.1746000	0.0617700	0.1938000	0.6123000	1.334000	14.49000	0.0033500	0.0138400	0.0145200	0.0068530	0.0111300	0.0017200	16.23000	29.89000	105.50000	740.7000	0.1503000	0.3904000	0.3728000	0.1607000	0.3693000	0.0961800	0.2951131	0.3821034
0.6372009	0.4447802	N23	23	0.6372009	0.4447802	NA	2401257.0	0.0000000	12.17700	15.87600	77.18900	462.8100	0.0803710	0.0390720	0.0085071	0.0080664	0.1560600	0.0570980	0.2719600	0.9711600	1.774100	21.31900	0.0057797	0.0074750	0.0054729	0.0047514	0.0176810	0.0019791	13.43000	20.29300	85.31000	562.9800	0.1070360	0.0755330	0.0375649	0.0331752	0.2344200	0.0667640	0.3199642	0.3000376
0.6952197	0.5985622	N24	24	0.6952197	0.5985622	NA	300940639.0	0.0000000	12.84333	15.87667	81.43333	513.2333	0.0777433	0.0336600	0.0028083	0.0054303	0.1369333	0.0539767	0.2490333	0.7847333	1.628333	20.46000	0.0046830	0.0038170	0.0018143	0.0034163	0.0163867	0.0013227	14.01000	19.21000	88.92667	609.5333	0.0978533	0.0503867	0.0122503	0.0220967	0.2139000	0.0596233	0.4474120	0.2807929
0.0000000	0.3421750	N25	25	0.0000000	0.3421750	NA	8910721.0	0.0000000	14.29000	16.82000	90.30000	632.6000	0.0642900	0.0267500	0.0072500	0.0062500	0.1508000	0.0537600	0.1302000	0.7198000	0.843900	10.77000	0.0034920	0.0037100	0.0048260	0.0036080	0.0153600	0.0013810	14.91000	20.65000	94.44000	684.6000	0.0856700	0.0503600	0.0386600	0.0333300	0.2458000	0.0612000	0.5465149	0.2983312
0.6795823	0.7156332	N26	26	0.6795823	0.7156332	NA	893526.0	0.0000000	13.50000	12.71000	85.69000	566.2000	0.0737600	0.0361400	0.0027580	0.0044190	0.1365000	0.0533500	0.2244000	0.6864000	1.509000	20.39000	0.0033380	0.0037460	0.0020300	0.0032420	0.0148000	0.0015660	14.97000	16.94000	95.48000	698.7000	0.0902300	0.0583600	0.0137900	0.0221000	0.2267000	0.0619200	0.5103685	0.2737304
0.6264635	0.0008187	N27	27	0.6264635	0.0008187	NA	8915.0	0.0000000	14.96000	19.10000	97.03000	687.3000	0.0899200	0.0982300	0.0594000	0.0481900	0.1879000	0.0585200	0.2877000	0.9480000	2.171000	24.87000	0.0053320	0.0211500	0.0153600	0.0118700	0.0152200	0.0028150	16.25000	26.19000	109.10000	809.8000	0.1313000	0.3030000	0.1804000	0.1489000	0.2962000	0.0847200	0.0921641	0.3549579
0.5876230	0.0000000	N28	28	0.5876230	0.0000000	NA	917896.0	0.0000000	13.71000	18.68000	88.73000	571.0000	0.0991600	0.1070000	0.0538500	0.0378300	0.1714000	0.0684300	0.3191000	1.2490000	2.284000	26.45000	0.0067390	0.0225100	0.0208600	0.0135200	0.0187000	0.0037470	15.11000	25.63000	99.43000	701.9000	0.1425000	0.2566000	0.1935000	0.1284000	0.2849000	0.0903100	0.0803571	0.3393867
0.5528728	0.0907782	N29	29	0.5528728	0.0907782	NA	23575258.3	0.2631579	13.09599	18.66447	84.69105	543.5605	0.0963203	0.0922289	0.0608997	0.0355610	0.1736053	0.0629233	0.3082421	1.1933829	2.159472	25.90987	0.0069000	0.0220297	0.0271489	0.0106714	0.0187188	0.0034155	14.83895	25.81263	97.36355	701.4434	0.1364624	0.2384346	0.2360724	0.1040430	0.2854684	0.0846041	0.1828726	0.3972866
0.5133601	0.2209132	N30	30	0.5133601	0.2209132	NA	23476092.6	0.2989691	13.32347	18.62412	86.28619	570.2082	0.0958060	0.0950003	0.0686730	0.0395061	0.1766701	0.0631502	0.3213639	1.1464495	2.220632	28.60928	0.0068605	0.0223363	0.0279565	0.0106736	0.0191032	0.0035494	15.17131	25.12505	99.28021	745.4598	0.1351007	0.2409355	0.2449421	0.1061320	0.2883474	0.0851176	0.2321924	0.4164238
0.4932039	0.3547114	N31	31	0.4932039	0.3547114	NA	48838196.0	0.4761905	14.55952	17.41476	94.38714	712.8095	0.0917943	0.0894352	0.0827719	0.0482523	0.1681143	0.0607324	0.3646714	0.9813190	2.446619	37.47924	0.0061516	0.0190227	0.0242373	0.0094161	0.0170319	0.0028763	16.91024	23.68143	110.28476	968.0762	0.1308514	0.2357662	0.2647710	0.1175410	0.2725714	0.0808624	0.3199845	0.4335055
0.4063064	0.4116395	N32	32	0.4063064	0.4116395	NA	911157302.0	1.0000000	21.10000	20.52000	138.10000	1384.0000	0.0968400	0.1175000	0.1572000	0.1155000	0.1554000	0.0566100	0.6643000	1.3610000	4.542000	81.89000	0.0054670	0.0207500	0.0318500	0.0146600	0.0102900	0.0022050	25.68000	32.07000	168.20000	2022.0000	0.1368000	0.3101000	0.4399000	0.2280000	0.2268000	0.0742500	0.3900611	0.4545824
0.4347895	0.0860170	N33	33	0.4347895	0.0860170	NA	15848615.5	0.4000000	14.21350	19.92450	92.29700	640.1650	0.0948765	0.1011755	0.0736000	0.0430940	0.1788700	0.0623210	0.3734000	1.2149100	2.617645	34.81400	0.0066280	0.0248040	0.0317900	0.0121240	0.0192105	0.0037842	16.26300	26.86100	106.70850	841.4550	0.1330650	0.2593640	0.2718400	0.1149160	0.2892950	0.0840550	0.1995680	0.4527368
0.3801900	0.1970649	N34	34	0.3801900	0.1970649	NA	10584515.0	0.4455446	13.99023	20.06644	91.23525	633.0941	0.0980265	0.1109529	0.0917531	0.0506595	0.1811634	0.0634276	0.3943634	1.2714248	2.824563	36.80066	0.0072961	0.0282688	0.0350737	0.0131708	0.0204602	0.0039207	16.07165	26.52277	106.30208	843.8059	0.1344217	0.2740756	0.2885514	0.1210808	0.2871802	0.0852774	0.2578535	0.4857521
0.3390217	0.3169053	N35	35	0.3390217	0.3169053	NA	32718713.7	0.6024096	15.27798	20.22325	99.77807	775.9434	0.0982083	0.1109277	0.1092437	0.0611492	0.1833108	0.0621029	0.4697386	1.2726578	3.193928	49.05439	0.0072157	0.0247359	0.0318245	0.0120915	0.0206929	0.0035904	17.99875	26.95313	118.43566	1090.2795	0.1364447	0.2726887	0.3158148	0.1319073	0.2953361	0.0847445	0.3409958	0.5096418
0.2881142	0.4237081	N36	36	0.2881142	0.4237081	NA	51669171.2	0.6000000	15.29480	20.95600	99.79520	793.9680	0.0943020	0.1046872	0.1063171	0.0608663	0.1821960	0.0612460	0.4642280	1.2885400	3.303120	50.57820	0.0063107	0.0235886	0.0294121	0.0111691	0.0206240	0.0033236	18.23476	27.96320	120.88000	1152.1560	0.1282120	0.2687320	0.3141836	0.1321000	0.2935680	0.0832208	0.4210566	0.5193592
0.2997246	0.5267026	N37	37	0.2997246	0.5267026	NA	4551125.0	0.5000000	17.03000	22.31000	112.97500	964.9000	0.0878250	0.1513500	0.1621150	0.0899400	0.1513500	0.0639950	0.5637000	1.0669500	4.669500	69.87450	0.0045100	0.0369050	0.0394050	0.0156900	0.0199400	0.0055770	20.11500	27.25500	141.18000	1357.7000	0.1086950	0.3549500	0.3834000	0.1762000	0.2466000	0.0896150	0.5047916	0.5551850
0.2016626	0.4678645	N38	38	0.2016626	0.4678645	NA	894335.0	0.0000000	12.43000	17.00000	78.60000	477.3000	0.0755700	0.0345400	0.0134200	0.0169900	0.1472000	0.0556100	0.3778000	2.2000000	2.487000	31.16000	0.0073570	0.0107900	0.0099590	0.0112000	0.0343300	0.0029610	12.90000	20.21000	81.76000	515.9000	0.0840900	0.0471200	0.0223700	0.0283200	0.1901000	0.0593200	0.4928099	0.5429805
0.8978652	0.8761455	N39	39	0.8978652	0.8761455	NA	873357.0	0.0000000	13.01000	22.22000	82.01000	526.4000	0.0625100	0.0193800	0.0015950	0.0018520	0.1395000	0.0523400	0.1731000	1.1420000	1.101000	14.34000	0.0034180	0.0022520	0.0015950	0.0018520	0.0161300	0.0009683	14.00000	29.02000	88.18000	608.8000	0.0812500	0.0343200	0.0079770	0.0092590	0.2295000	0.0584300	0.6760216	0.4745825
0.8439500	0.9272829	N40	40	0.8439500	0.9272829	NA	873357.0	0.0000000	13.01000	22.22000	82.01000	526.4000	0.0625100	0.0193800	0.0015950	0.0018520	0.1395000	0.0523400	0.1731000	1.1420000	1.101000	14.34000	0.0034180	0.0022520	0.0015950	0.0018520	0.0161300	0.0009683	14.00000	29.02000	88.18000	608.8000	0.0812500	0.0343200	0.0079770	0.0092590	0.2295000	0.0584300	0.6760216	0.4745825
0.2568029	0.2380713	N41	41	0.2568029	0.2380713	NA	43317541.8	0.5862069	14.41610	21.15345	93.99345	675.4379	0.0986752	0.1086186	0.0938924	0.0536076	0.1801552	0.0615779	0.4449793	1.3587690	3.201448	42.32124	0.0085912	0.0269869	0.0353378	0.0148876	0.0209721	0.0036257	16.52083	27.11862	109.90207	894.4517	0.1359345	0.2504324	0.2792334	0.1234548	0.2757172	0.0801814	0.2883097	0.5477604
0.1886496	0.3492252	N42	42	0.1886496	0.3492252	NA	39713198.7	0.5616438	14.87360	20.94918	97.21534	727.2630	0.1007386	0.1137412	0.1108364	0.0610652	0.1863685	0.0632308	0.4827863	1.4852329	3.341548	47.77570	0.0084535	0.0281595	0.0358687	0.0136363	0.0227738	0.0042736	17.29012	27.63205	114.31767	992.0370	0.1379126	0.2613212	0.3075953	0.1255544	0.2884342	0.0843730	0.3550034	0.5691102
0.1689766	0.4723279	N43	43	0.1689766	0.4723279	NA	34306209.3	0.6538462	16.06606	21.74596	105.45250	862.2731	0.0971142	0.1237775	0.1221242	0.0682241	0.1872423	0.0626077	0.5695192	1.4395923	4.078096	61.13267	0.0072560	0.0320094	0.0372661	0.0137623	0.0221185	0.0043778	19.00894	28.60635	126.84442	1211.7596	0.1330125	0.3177973	0.3577069	0.1444533	0.2971288	0.0882800	0.4384754	0.5873970
0.2222091	0.5737410	N44	44	0.2222091	0.5737410	NA	19811714.6	0.6400000	15.76132	21.97520	104.32840	850.0120	0.0984096	0.1449108	0.1514876	0.0772068	0.1949880	0.0665340	0.6078200	1.3669880	4.576720	66.31288	0.0068069	0.0352177	0.0438014	0.0134861	0.0235224	0.0050477	18.80972	28.40880	128.24480	1213.3520	0.1325032	0.3728040	0.4403420	0.1531428	0.3124640	0.0969368	0.5219885	0.6073919
0.3069179	0.6516061	N45	45	0.3069179	0.6516061	NA	84667401.0	1.0000000	13.73000	22.61000	93.60000	578.3000	0.1131000	0.2293000	0.2128000	0.0802500	0.2069000	0.0768200	0.2121000	1.1690000	2.061000	19.21000	0.0064290	0.0593600	0.0550100	0.0162800	0.0196100	0.0080930	15.03000	32.01000	108.80000	697.7000	0.1651000	0.7725000	0.6943000	0.2208000	0.3596000	0.1431000	0.5903791	0.6380966
0.0832546	0.4545349	N46	46	0.0832546	0.4545349	NA	18666783.0	0.5625000	14.25956	19.22750	93.63375	657.7750	0.1003150	0.1230275	0.1143862	0.0580681	0.2028312	0.0659688	0.4925000	1.4001125	3.524875	46.62500	0.0098769	0.0376344	0.0438537	0.0151248	0.0270600	0.0057202	16.41937	24.51187	109.17375	870.0562	0.1336938	0.2839950	0.3022356	0.1227006	0.3150938	0.0884225	0.3771646	0.6387061
0.1033860	0.5708874	N47	47	0.1033860	0.5708874	NA	18230737.0	0.6285714	15.49009	20.75429	101.91514	804.6686	0.1006531	0.1308157	0.1289347	0.0700857	0.1970343	0.0649260	0.6403657	1.5062114	4.626314	69.95743	0.0085898	0.0372216	0.0462445	0.0166229	0.0252451	0.0052977	18.44783	27.04571	123.17400	1155.2086	0.1350966	0.3186271	0.3576463	0.1426080	0.3080829	0.0917754	0.4624861	0.6535477
0.1883090	0.6719276	N48	48	0.1883090	0.6719276	NA	18064352.7	0.6250000	15.32775	21.80025	101.35600	804.7600	0.1007560	0.1472350	0.1566078	0.0769632	0.1951200	0.0673970	0.6180150	1.4266125	4.482450	69.79552	0.0081543	0.0395294	0.0500554	0.0154782	0.0233167	0.0058689	18.47563	28.10550	124.17650	1199.5025	0.1376388	0.3535958	0.4135202	0.1531428	0.3023725	0.0968892	0.5381257	0.6710598
0.3051285	0.7423285	N49	49	0.3051285	0.7423285	NA	15271760.3	0.8461538	17.99900	23.62385	120.38462	1100.2385	0.1091492	0.1871900	0.2156385	0.1084954	0.2081692	0.0692469	0.5882385	1.3847769	4.485769	76.60677	0.0075922	0.0406600	0.0514523	0.0158008	0.0219585	0.0053744	22.17631	33.09615	151.80923	1682.3692	0.1556308	0.5172900	0.5906846	0.2181923	0.3527000	0.1071808	0.6395179	0.6934180
0.4232847	0.7851556	N50	50	0.4232847	0.7851556	NA	6166328.7	1.0000000	19.13000	23.43667	129.16667	1183.5333	0.1140000	0.2550333	0.2505000	0.1325900	0.2140000	0.0737667	0.5795000	1.0879667	4.505000	71.81667	0.0066080	0.0500033	0.0473000	0.0164533	0.0153367	0.0052077	23.30667	33.30667	159.98667	1719.7000	0.1749333	0.7679667	0.7219333	0.2764667	0.3535667	0.1246000	0.7022116	0.7054340
0.4882285	1.0000000	N51	51	0.4882285	1.0000000	NA	899987.0	1.0000000	25.73000	17.46000	174.20000	2010.0000	0.1149000	0.2363000	0.3368000	0.1913000	0.1956000	0.0612100	0.9948000	0.8509000	7.222000	153.10000	0.0063690	0.0424300	0.0426600	0.0150800	0.0233500	0.0033850	33.13000	23.58000	229.30000	3234.0000	0.1530000	0.5937000	0.6451000	0.2756000	0.3690000	0.0881500	0.7385838	0.7096714
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0.3057724	0.8561349	N55	55	0.3057724	0.8561349	NA	12852619.8	0.5625000	14.68056	19.91187	98.36813	734.2313	0.1100681	0.1982731	0.1952350	0.0893375	0.2154000	0.0770612	0.5360250	1.3354625	3.893625	58.17175	0.0091695	0.0529875	0.0630375	0.0174625	0.0294800	0.0090179	17.69969	26.92625	120.78938	1121.9437	0.1482075	0.4655419	0.5132375	0.1763600	0.3518188	0.1120956	0.6488489	0.7413141
0.4594123	0.8925995	N56	56	0.4594123	0.8925995	NA	8456946.7	0.8333333	16.75417	21.70083	113.40833	912.7417	0.1049900	0.2327783	0.2388667	0.1068642	0.2194667	0.0738367	0.6821583	1.9094250	5.626333	79.53083	0.0062604	0.0648680	0.0715117	0.0190058	0.0305158	0.0073741	20.43067	30.31667	142.73833	1363.8917	0.1438133	0.6594075	0.6793500	0.2141333	0.3799333	0.1194700	0.7254413	0.7622228
0.3892211	0.8519800	N57	57	0.3892211	0.8519800	NA	8611555.0	1.0000000	25.22000	24.91000	171.50000	1878.0000	0.1063000	0.2665000	0.3339000	0.1845000	0.1829000	0.0678200	0.8973000	1.4740000	7.382000	120.00000	0.0081660	0.0569300	0.0573000	0.0203000	0.0106500	0.0058930	30.00000	33.62000	211.70000	2562.0000	0.1573000	0.6076000	0.6476000	0.2867000	0.2355000	0.1051000	0.7241484	0.7025255
0.9864304	0.7426135	N58	58	0.9864304	0.7426135	NA	86355.0	1.0000000	22.27000	19.67000	152.80000	1509.0000	0.1326000	0.2768000	0.4264000	0.1823000	0.2556000	0.0703900	1.2150000	1.5450000	10.050000	170.00000	0.0065150	0.0866800	0.1040000	0.0248000	0.0311200	0.0050370	28.40000	28.01000	206.80000	2360.0000	0.1701000	0.6997000	0.9608000	0.2910000	0.4055000	0.0978900	0.9311718	0.7784275
0.1294149	0.8502782	N59	59	0.1294149	0.8502782	NA	859711.0	0.0000000	8.88800	14.64000	58.79000	244.0000	0.0978300	0.1531000	0.0860600	0.0287200	0.1902000	0.0898000	0.5262000	0.8522000	3.168000	25.44000	0.0172100	0.0936800	0.0567100	0.0176600	0.0254100	0.0219300	9.73300	15.67000	62.56000	284.4000	0.1207000	0.2436000	0.1434000	0.0478600	0.2254000	0.1084000	0.5919389	0.7977983
0.6627955	0.9858353	N60	60	0.6627955	0.9858353	NA	859471.0	0.0000000	9.02900	17.33000	58.79000	250.5000	0.1066000	0.1413000	0.3130000	0.0437500	0.2111000	0.0804600	0.3274000	1.1940000	1.885000	17.67000	0.0095490	0.0860600	0.3038000	0.0332200	0.0419700	0.0095590	10.31000	22.65000	65.50000	324.7000	0.1482000	0.4365000	1.2520000	0.1750000	0.4228000	0.1175000	0.6948123	0.8442810
0.3122399	0.9670893	N61	61	0.3122399	0.9670893	NA	485119202.0	0.5000000	15.91500	22.64500	105.26500	799.5000	0.0940850	0.1411000	0.1522000	0.0659950	0.1511000	0.0652900	0.7053500	1.7185000	4.063500	67.82000	0.0194460	0.0959750	0.1217000	0.0334900	0.0312600	0.0177100	16.92000	25.10000	111.05000	894.1500	0.1120650	0.2132500	0.2511500	0.1060000	0.1937500	0.0780850	0.6635286	0.8227825
0.2078948	0.9004729	N62	62	0.2078948	0.9004729	NA	859711.0	0.0000000	8.88800	14.64000	58.79000	244.0000	0.0978300	0.1531000	0.0860600	0.0287200	0.1902000	0.0898000	0.5262000	0.8522000	3.168000	25.44000	0.0172100	0.0936800	0.0567100	0.0176600	0.0254100	0.0219300	9.73300	15.67000	62.56000	284.4000	0.1207000	0.2436000	0.1434000	0.0478600	0.2254000	0.1084000	0.5919389	0.7977983
0.5727938	0.9560023	N63	63	0.5727938	0.9560023	NA	859045.0	0.7500000	15.37225	22.51500	103.46500	771.8500	0.1005775	0.2118500	0.2320750	0.0803350	0.2300500	0.0743275	0.6375000	2.1345000	5.974250	67.62250	0.0068015	0.1012575	0.1516325	0.0292900	0.0478175	0.0104412	17.77500	30.73500	125.25000	1017.5250	0.1324750	0.6259750	0.7972250	0.1945500	0.4310000	0.1170500	0.7326821	0.8170121
0.5569509	0.8466482	N64	64	0.5569509	0.8466482	NA	84501001.0	1.0000000	12.46000	24.04000	83.97000	475.9000	0.1186000	0.2396000	0.2273000	0.0854300	0.2030000	0.0824300	0.2976000	1.5990000	2.039000	23.94000	0.0071490	0.0721700	0.0774300	0.0143200	0.0178900	0.0100800	15.09000	40.68000	97.65000	711.4000	0.1853000	1.0580000	1.1050000	0.2210000	0.4366000	0.2075000	0.7271720	0.7927863
0.2647630	0.0496826	N65	65	0.2647630	0.0496826	NA	8760572.0	0.5000000	18.92050	16.90500	126.14000	1399.6000	0.1107000	0.1557500	0.3654500	0.1190350	0.2098000	0.0741050	1.8487500	2.0700000	13.026500	287.72500	0.0122100	0.0617900	0.2299450	0.0334300	0.0416450	0.0171580	19.56500	18.98000	129.77000	1439.7500	0.1217000	0.2144000	0.5708500	0.1583000	0.2378000	0.0905750	0.8816149	0.8979599
0.2001185	0.0067192	N66	66	0.2001185	0.0067192	NA	911296202.0	1.0000000	27.42000	26.27000	186.90000	2501.0000	0.1084000	0.1988000	0.3635000	0.1689000	0.2061000	0.0562300	2.5470000	1.3060000	18.650000	542.20000	0.0076500	0.0537400	0.0805500	0.0259800	0.0169700	0.0045580	36.04000	31.37000	251.20000	4254.0000	0.1357000	0.4256000	0.6833000	0.2625000	0.2641000	0.0742700	0.8817185	0.8905553
0.1062707	0.1651024	N67	67	0.1062707	0.1651024	NA	46479581.5	1.0000000	15.80000	22.17500	110.64000	815.5500	0.1355500	0.3146500	0.3084000	0.1328000	0.2751500	0.0894300	0.7136500	1.5205000	6.047000	71.81500	0.0097450	0.0714650	0.0828550	0.0223000	0.0692900	0.0075975	19.14000	29.11000	134.58500	1095.3500	0.1868500	0.7413500	0.7275000	0.2541500	0.6039000	0.1363200	0.9093795	0.8356010
0.1701194	0.0892239	N68	68	0.1701194	0.0892239	NA	202786298.2	1.0000000	22.27600	21.85800	152.57600	1678.4200	0.1276800	0.2532800	0.3454400	0.1590400	0.2373400	0.0718220	1.6712600	1.7886000	12.506200	288.88600	0.0127840	0.0644900	0.0875900	0.0205740	0.0497700	0.0068208	25.69000	26.41000	177.95400	2203.3400	0.1586400	0.4968600	0.6077400	0.2310200	0.3917800	0.0964500	0.9224915	0.8633097

Plot summerized information per node:

library(plotly)
fig <- ggplot(combined_dat, aes(x = x, y = y, xend = xend, yend = yend, 
                                text=sprintf("Node: %s<br>Concavity: %s", Nodename, concavity_se))) +
  geom_edges(aes(), color = "grey75") +
  geom_nodes(aes(color = diagnosis, size= texture_se )) +
  scale_color_gradient(low = "blue", high = "red") +
  # geom_nodelabel_repel(aes(label = name), box.padding = unit(1, "lines")) +
  theme(axis.text = element_blank(),
        axis.title = element_blank(),
        panel.background = element_rect(fill = "black"),
        panel.grid = element_blank())
fig

plotly::ggplotly(fig, tooltip = "text" , width = 1000, height = 800) %>% 
  highlight(., on = "plotly_selected", off = "plotly_doubleclick")  %>% subplot()

Show groupings by selecting nodes

Data processing

scale_zero_to_one <- function(vector){

  a <- vector - min(vector)
  b <- max(vector) - min(vector)

  return(a/b)
}

combined_dat <- combined_dat %>% mutate(symmetry_group = scale_zero_to_one(symmetry_mean) %>%  cut(.,  c(-0.1,0.20, 0.40, 0.60, 0.80, 1.01)) )
levels(combined_dat$symmetry_group) <- c("very low", "low", "medium", "high", "extreme")

Visualization

d <- highlight_key(combined_dat, ~symmetry_group)
p <- ggplot(d, aes(x = x, y = y, xend = xend, yend = yend, text=sprintf("Node: %s<br>Symmetry: %s", Nodename, symmetry_group))) +
  geom_edges(aes(), color = "grey75") +
  geom_nodes(aes(color = diagnosis, size= texture_se )) +
  scale_color_gradient(low = "blue", high = "red") # +
  # geom_nodelabel_repel(aes(label = name), box.padding = unit(1, "lines")) +
  # theme(axis.text = element_blank(),
  #       axis.title = element_blank(),
  #       panel.background = element_rect(fill = "black"),
  #       panel.grid = element_blank())
gg <- ggplotly(p, tooltip = "text", width = 1000, height = 800) %>% 
  highlight(., on = "plotly_selected", off = "plotly_doubleclick") %>% 
  subplot() 
highlight(gg, dynamic = TRUE)

Some styling:

# supply custom colors to the brush
# cols <- toRGB(RColorBrewer::brewer.pal(3, "Dark2"), 0.5)
# highlight(gg, on = "plotly_hover", color = cols, dynamic = TRUE)
plot_ly(d, x= ~diagnosis,  type = "histogram", width = 1000, height = 800)

Possible extensions

Lasso

Bibliography

Singh, Gurjeet, Facundo Mémoli, and Gunnar E Carlsson. 2007. “Topological Methods for the Analysis of High Dimensional Data Sets and 3d Object Recognition.” In SPBG, 91–100.

Knowledge Lab AG, linda.decave@k-lab.ch ↩
Knowledge Lab AG, marco.wirthlin@k-lab.ch ↩

satRdays: TDA

A small showcase of the mapper algorithm

Linda de Cave¹

Marco Wirthlin²

13 March, 2020

What‘s TDA?

How to use it?

The steps of the mapper algorithm:

The data set

Linking the output from the mapper to your data set.

Visualizations

D3 (not recommended)

ggnetwork

Plot summerized information per node:

Show groupings by selecting nodes

Data processing

Visualization

Some styling:

Possible extensions

Bibliography

satRdays: TDA

A small showcase of the mapper algorithm

Linda de Cave1

Marco Wirthlin2

13 March, 2020

What‘s TDA?

How to use it?

The steps of the mapper algorithm:

The data set

Linking the output from the mapper to your data set.

Visualizations

D3 (not recommended)

ggnetwork

Plot summerized information per node:

Show groupings by selecting nodes

Data processing

Visualization

Some styling:

Possible extensions

Bibliography

Linda de Cave¹

Marco Wirthlin²